L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a parallelogram is a rhombus or a rectangle?

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Presentation transcript:

L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a parallelogram is a rhombus or a rectangle?

 Each diagonal of a rhombus bisects two angles of the rhombus.

 The diagonals of a rhombus are perpendicular.

 MNPQ is a rhombus and  Find the measure of the numbered angles.

 Find the measures of the numbered angles in the rhombus below.

 The diagonals of a rectangle are congruent.

 Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y – 5.

Find the length of the diagonals of GFED if FD = 5y - 9 and GE = y + 5.

 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.

 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

 Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain. ◦ The quadrilateral has congruent diagonals and one angle of 60 degrees. ◦ The quadrilateral has perpendicular diagonals and four right angles.

 A diagonal of a parallelogram bisects two angles of the parallelogram. Is it possible for the parallelogram to have sides of lengths 5, 6, 5, and 6? Explain.

 Community Service Builders use properties of diagonals to “square up” rectangular shapes like building frames and playing-field boundaries. Suppose you are on the volunteer building team at the right. You are helping to lay out a rectangular patio. Explain how to use properties of diagonals to locate the four corners.

 Pgs #s 2 – 20 even, 48 – 50 all.